Rotary printing machines which have cylinders with axial grooves are subjects to shocks and vibration. When two cylinder grooves of printing cylinders, for example rubber blanket cylinders of an offset machine run off against each other, a shock or impact results which, on the printed subject matter, may be noticed as a strip of different intensity of inking. This problem arises particularly in modern high-speed rotary printing machines. It has been proposed to cover the cylinder groove--see the referenced U.S. Pat. No. 4,403,549, Matuschke. Other proposals have been made to dampen impacts and shocks which impair the quality of the printed subject matter. Fillers as known heretofore usually extended over the entire length of the cylinder groove. This causes difficulty in handling the machine or machine set-up; in manufacture, also, difficulties arise and such fillers may become expensive, particularly with long cylinders. Some improvement was obtained, although further improvement still is desirable.